1. It's a kind of shopping by computer.

2. It's a kind of shopping on the computer.
3. It's a kind of shopping on-line.
4. It's a kind of on-line shopping?
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Are they all the same? Can we use 'on the computer' instead of 'by computer'?

What exactly is this for, my dear? I would say that 3 & 4 are the same for sure. Don't use number 1, unless you have to. I really don't think that number 1 makes sense. 2 is ok, but again, use 3 & 4. Those make the most sense. Hope this helps!

All four are correct.

The phrase "on the computer" is more common, but "by computer" is not incorrect.

Yes, all four statements are essentially conveying the same idea, which is that the shopping is done using a computer. However, there are slight differences in the phrasing used.

The phrases "shopping by computer" and "shopping on the computer" are quite similar because they both imply that the computer is the medium through which the shopping is conducted. However, "shopping by computer" emphasizes the use of the computer as the tool or means for shopping, whereas "shopping on the computer" simply indicates that the shopping is taking place using the computer as a platform.

On the other hand, "shopping online" and "online shopping" mean the same thing, which is that the shopping is done over the internet. These phrases specifically highlight that the transactions occur digitally, without the need for physical presence in a store.

In summary, all four phrases convey the same concept of using a computer for shopping, with slight variations in emphasis and wording.